THE SCHEME OF CHARACTERS IN SL2

Michael Heusener, Joan Porti

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Abstract

The aim of this article is to study the SL2(C)–character scheme of a finitely generated group. Given a presentation of a finitely generated group Γ, we give equations defining the coordinate ring of the scheme of SL2(C)–characters of Γ (finitely many equations when Γ is finitely presented). We also study the scheme of abelian and non-simple representations and characters. Finally we apply our results to study the SL2(C)–character scheme of the Borromean rings.

Original languageEnglish
Pages (from-to)6283-6313
Number of pages31
JournalTransactions of the American Mathematical Society
Volume376
Issue number9
DOIs
Publication statusPublished - 9 May 2023

Keywords

  • Representation variety, character variety

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